# Worksheet on Remainder Theorem

Practice the questions given in the worksheet on Remainder Theorem.

1. Use the Remainder Theorem, find the remainder when 4x$$^{3}$$ - 3x$$^{2}$$ + 2x - 4 is divided by x + 1.

2. If p(y) = y$$^{3}$$ + y$$^{2}$$ - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).

3. Find the remainder (without division) when

(a) x$$^{2}$$ - 2x + 4 is divided by x - 1

(b) 2x$$^{3}$$ - 3x$$^{2}$$ + 7x - 8 is divided by x - 1

4. Use the Remainder Theorem, find the remainder when x$$^{4}$$ - 3x$$^{2}$$ + 4x - 12 is divided by x - 3.

5. Find the remainder (without division) when

(a) x$$^{3}$$ + 4x + 2 is divisible by x + 2

(b) 4x$$^{3}$$ - 3x$$^{2}$$ + 5x + 4 is divided by 2x + 1

(c) 4x$$^{3}$$ + 5x$$^{2}$$ + 6x - 7 is divided by 2x - 1

6. What number should be added to x$$^{2}$$ + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

7. Use the Remainder Theorem, find the remainder when 4x$$^{3}$$ - 3x$$^{2}$$ + 2x - 4 is divided by x + 1.

8. What number should be subtracted from 3x$$^{2}$$ + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

9. Use the Remainder Theorem, find the remainder when x$$^{6}$$ + 3x$$^{2}$$ + 10 is divided by x - 2.

10.  Find a if the remainder is a when x$$^{3}$$ + 3x$$^{2}$$ - ax + 3 is divided by x - 2.

11. If the polynomials ax$$^{3}$$ + 4x$$^{2}$$ + 3x – 4 and x$$^{3}$$ - 4x + a leave the same remainder when divided by (x - 3), find the value of a.

12. Find the value of k if the remainder is -3 when kx$$^{3}$$ + 8x$$^{2}$$ - 4x + 10 is divided by x +1.

13. If both ax$$^{3}$$ + 2x$$^{2}$$ - 3 and x$$^{2}$$ - ax + 4 leave the same remainder when divided by x - 2, find a.

Answers for the worksheet on Remainder Theorem are given below:

1. -13

2. 31, a$$^{3}$$ + a$$^{2}$$ - 2a + 1

3. (a) 3

(b) -2

4. 54

5. (a) -14

(b) $$\frac{1}{4}$$

(c) -$$\frac{9}{4}$$

6. -11

7. -13

8. $$\frac{21}{4}$$

9. 86

10. $$\frac{23}{3}$$

11. a = -1.

12. 25

13. $$\frac{3}{10}$$

● Factorization

From Worksheet on Remainder Theorem to HOME

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

Dec 04, 23 02:14 PM

Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

2. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 04, 23 01:50 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…